scholarly journals Bifurcation of time-periodic solutions for the incompressible flow of nematic liquid crystals in three dimension

2019 ◽  
Vol 9 (1) ◽  
pp. 1315-1332 ◽  
Author(s):  
Hengyan Li ◽  
Xin Zhao ◽  
Weiping Yan
Keyword(s):  
Liquid Crystals ◽  
Periodic Solutions ◽  
Incompressible Flow ◽  
Nematic Liquid Crystals ◽  
Dynamical Behavior ◽  
Time Dependent ◽  
Three Dimension ◽  
Time Periodic Solutions ◽  
External Forces ◽  
Time Periodic

Abstract This paper is devoted to the study of the dynamical behavior for the 3D incompressible flow of liquid crystals. We prove that this system under smooth external forces possesses time dependent periodic solutions, bifurcating from a steady solution.

Time-periodic solutions of symmetric hyperbolic systems

2020 ◽  
Vol 17 (04) ◽  
pp. 707-726
Author(s):  
Masashi Ohnawa ◽  
Masahiro Suzuki
Keyword(s):  
Periodic Solutions ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Unique Existence ◽  
Periodic Problems ◽  
Time Periodic Solutions ◽  
External Forces ◽  
Initial Boundary Value ◽  
Time Periodic

We prove the unique existence of time-periodic solutions to general hyperbolic equations with periodic external forces autonomous or nonautonomous over a domain bounded by two parallel planes, provided that all the characteristics with respect to the direction normal to the planes have the same sign. It is also shown that global-in-time solutions to initial-boundary value problems coincide with the solutions to corresponding time-periodic problems after a finite time. We devote one section to the reformulation of several realistic problems and see our results have wide applicability.

scholarly journals ON TIME PERIODIC SOLUTIONS TO THE GENERALIZED BBM-BURGERS EQUATION WITH TIME-DEPENDENT PERIODIC EXTERNAL FORCE

2020 ◽  
Vol 25 (2) ◽  
pp. 184-197
Author(s):  
Yinxia Wang
Keyword(s):  
Periodic Solutions ◽  
External Force ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Space Dimension ◽  
Burgers Equation ◽  
Time Dependent ◽  
Contraction Mapping Theorem ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper, we consider the generalized BBM-Burgers equation with periodic external force in Rn. Existence and uniqueness of time periodic solutions that have the same period as the external force are established in some suitable function space for the space dimension n≥ 3. Moreover, we also discuss the time asymptotic stability of the time periodic solution. The proof is mainly based on the contraction mapping theorem and continuous argument.

On the time periodic thermistor problem

2004 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
WALTER ALLEGRETTO ◽  
YANPING LIN ◽  
SHUQING MA
Keyword(s):  
Periodic Solutions ◽  
Degree Theory ◽  
Time Behaviour ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Galerkin Approximations ◽  
Long Time ◽  
Finite Dimensionality ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

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